If the integral 525 ∫_0^((π)/2) sin 2 x cos^(11/2) x(1+ Cos^(5/2) x)^(1/2) d x is equal to (n √ 2 -64), then n is equal to ____

If the integral $\displaystyle 525 \int_0^{\frac{\pi}{2}} \sin 2 x \cos ^{\frac{11}{2}} x\left(1+\operatorname{Cos}^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x$ is equal to $\displaystyle (n \sqrt{2}-64)$, then $\displaystyle n$ is equal to $\displaystyle \_\_\_\_$